The invention relates to double-ended tuning forks and particularly to double-ended tuning forks as used in the construction of accelerometer devices.
Non-linearities in accelerometer outputs can lead to significant measurement errors in the absence of compensation circuitry. Generally, non-linearity errors occur when inputs are near the full-scale range of the instrument or there is vibration along the input axis, but they may also occur simply because the particular application requires an extremely linear response. Instruments using double-ended tuning forks, or DETFs, as inertial reaction force sensors are particularly vulnerable to errors introduced by non-linearities. The inherent non-linearity of a force sensor or accelerometer using a single DETF is typically higher than that of a common high-accuracy, analog, force-rebalance accelerometer, for example, those described in U.S. Pat. Nos. 3,702,073 and 4,250,757.
A DETF-based accelerometer, however, possesses real advantages over other accelerometers. For example, a DETF-based accelerometer typically provides smaller size, lower power consumption, and ease of interface to digital systems. Compensation of DETF-based accelerometer non-linearity provides all these benefits without a serious performance penalty.
Practical accelerometers in the past have used software compensation of non-linearities, or a combination of software and hardware compensation. Software compensation is not viable for other than constant or slowly varying acceleration inputs because the processor cannot execute the compensation commands at frequencies high enough to keep pace with the accelerometer inputs.
One combined software and hardware compensation approach that has been used is to infer the input acceleration based on models that depend on the difference frequency between two DETFs. This approach assumes that the DETFs have been designed to possess the same second-order non-linearity when subjected to purely axial forces.
The DETFs may be attached either to one or to two independent proof masses. Dual-proof-mass accelerometers are really two separate accelerometers in the same package. Using dual-proof-mass accelerometers leads to difficult matching problems to ensure that the responses of the two accelerometers track when the accelerometer sees vibration or other rapidly-changing inputs.
A common approach to avoiding the common mode tracking problems created by using two accelerometers in one package is to attach two DETFs to a single proof mass, arranging them so that displacement of the proof mass under loading places one of them in tension and the other in compression. In practical accelerometers, the exact arrangement of the DETFs is dictated by several factors. One factor is the need to incorporate stress isolation, for example, see U.S. Pat. No. 4,766,768, incorporated herein by reference. Another factor is the necessity of having both DETFs on the same side of the proof mass, for example, monolithic silicon accelerometers built with epitaxial layer DETFs. Other reasons which do not consider the effect of the DETF positions on the non-linearity of the accelerometer also dictate the exact arrangement of the DETFs, for example, manufacturing tolerances or other processing limitations, or size restrictions.
FIG. 1 shows a plan view of a DETF accelerometer constructed according to the prior art techniques. The accelerometer of FIG. 1 combines a proof mass 2 and DETFs 4, 6. DETFs 4, 6, however, are positioned at much different distances 14, 16 from the centerline 8 of the hinges 10, 12. Thus, the non-linearities of the two DETFs do not cancel effectively when the difference frequency is formed, even when the DETFs are designed for the ideal case in which second-order non-linearity, K2, values cancel when subjected to purely axial forces. The lack of second-order non-linearity cancellation when the difference frequency is formed causes measurement errors and raises difficulties when DETF force sensors and accelerometers are used in applications requiring a high degree of linearity.
General information on the design of vibrating beam accelerometers may be found in the text by Lawrence entitled Modern Inertial Technology: Navigation, Guidance and Control, Copyright 1993, Springer-Verlag, N.Y.
The invention recognizes and accounts for the fact that the deformation of the DETFs in a two-DETF, single-proof-mass accelerometer are not purely axial extensions or compressions, but also involve rotations and transverse displacements of the ends of the DETFs. The rotations and displacements create additional changes in the tine stiffnesses beyond those that occur due to simple stress stiffening effects. The effect of the additional stiffness changes is to alter the linearities of the DETFs, so that the second-order effects such as those due to, for example, Euler buckling loads, do not cancel when the difference frequency is formed.
According to one aspect of the present invention, the present invention includes various embodiments which overcome the problems of the prior art by providing positioning of the two DETFs which minimizes or eliminates second-order, K2, non-linearity effects.
According to another aspect of the present invention, the invention provides methods for positioning the dual-DETFs such that second-order non-linearities of the two DETFs will be equal under the deformations that they actually undergo in use. Thus, the present invention provides cancellation of the composite second-order non-linearity.
According to yet another aspect of the present invention, the present invention provides single processing etching mask change to fine tune the position of the two DETFs which minimizes both individual DETF second-order non-linearity and the composite common mode second-order non-linearity.
According to still another aspect of the present invention, the present invention further provides various physical embodiments which place the two DETFs such that the individual DETF second-order values are a minimum and the composite second-order terms cancel.